The video files I have are in 4:3 but using letter heads, I have the option to out-put from After Effects, an 16:9 anamorphic uncompressed AVI file by squeezing the original file. The video originate from DV but all graphic work and text is made in After Effect and out put as an uncompressed file...

Will I gain any quality by compressing a 16:9 file? When compressing the 4:3 file, I am compressing a lot of black… "The letter head".
What do you guys think???

Also, what about compability? I have noticed that a lot of commercial DVD's no longer offer real 16:9 (I have a 16:9 TV) so maybe there is some issues regarding 16:9 format?

Resizing the image to 16:9 will take time and will not improve quality (in fact, it will make the image look worse; slightly blurred).

You should always avoid resizing the video. Resize only if you are mixing two type of footage (ex., some scenes shot in 4:3 and some in 16:9). If all the footage is 4:3, leave it in 4:3.

Due to the way MPEG compression works, the black bars take almost no space at all (they don't move, so temporal compression eliminates them from P- and B-pictures, and they have no high frequencies, so they are also highly compressed in I-pictures).

You can test this by compressing two pictures in JPEG (which also uses DCT for compression): one with black bars, and one without. The difference in size will usually be less than 2%.